Circle packing in a square

Circle packing in a square is a packing problem in recreational mathematics, where the aim is to pack n unit circles into the smallest possible square.

Equivalently, the problem is to arrange n points in a unit square aiming to get the greatest minimal separation, dn, between points.

[1] To convert between these two formulations of the problem, the square side for unit circles will be L = 2 + ⁠2/dn⁠.

Solutions (not necessarily optimal) have been computed for every N ≤ 10,000.

[2] Dense packings of circles in non-square rectangles have also been the subject of investigations.